Understand the idea
Highly correlated inputs can exchange coefficient weight with little change in predictions. This makes individual effects difficult to interpret.
Python skill: Creates a small reproducible perturbation for each observation.
Meet the syntax
rng.normal(0, .001, len(df))
pd.Series(model.coef_, index=X.columns)rng.normal(0, .001, len(df))- Creates a small reproducible perturbation for each observation.
pd.Series(model.coef_, index=X.columns)- Labels the jointly fitted coefficients, including the near-duplicate input.
Follow the code
Use the numbered comments to connect each Python block to the workflow above.
from sklearn.linear_model import LinearRegression
rng=np.random.default_rng(42)
X=pd.DataFrame({'distance':df.distance,'near_copy':df.distance+rng.normal(0,.001,len(df))})
model=LinearRegression().fit(X,df.duration)
answer=pd.Series(model.coef_,index=X.columns)
This practice: Read and run the Python. Next: Change · Correlated predictors and unstable coefficients.
Given data · MIX60
60 observations. One synthetic delivery observation generated for practice. The dataframe df is supplied afresh for each Run.
| distance | weight | service | weekend | duration |
|---|---|---|---|---|
| 15.7052 | 6.75035 | standard | 0 | 61.7704 |
| 9.33869 | 4.81674 | express | 1 | 35.1694 |
| 17.3134 | 5.73931 | economy | 0 | 59.0766 |
| 14.25 | 7.69699 | standard | 1 | 56.5785 |
| 2.78937 | 6.42024 | express | 0 | 19.5577 |
| 19.5368 | 5.62508 | economy | 1 | 77.0289 |
| 15.4617 | 5.68023 | standard | 0 | 56.8109 |
| 15.9352 | 3.17871 | express | 1 | 52.08 |
Column meanings and units
Distance, weight and duration use the fixture’s numeric units; no kilometres, kilograms, minutes or other physical units are specified. RMSE is reported in the same synthetic duration units as the target.
These deterministic teaching observations do not describe real deliveries. Service effects and the alternating weekend flag are built into the generated response; they do not establish real-world causal effects.
distancefloat64- Numeric delivery-distance inputUnit / values: Synthetic distance units; physical unit unspecified
weightfloat64- Numeric parcel-weight inputUnit / values: Synthetic weight units; physical unit unspecified
servicestr- Delivery-service categoryUnit / values: standard / express / economy
weekendint64- Binary weekend input, alternating in the fixtureUnit / values: 0 / 1 indicator
durationfloat64- Numeric delivery-duration targetUnit / values: Synthetic duration units; physical unit unspecified
Your task · Follow
Fit a line using distance and a near-copy of distance. Store the two coefficients in answer, labelled by their feature names.
Hint 1 — Think
Nearly duplicate predictors can share the same predictive contribution in unstable proportions.
Hint 2 — Tools
Seeded noise, dataframe construction and LinearRegression.coef_.
Hint 3 — Approach
Create the near-copy column, fit both columns together and label the resulting coefficients.
Explained solution
from sklearn.linear_model import LinearRegression
rng=np.random.default_rng(42)
X=pd.DataFrame({'distance':df.distance,'near_copy':df.distance+rng.normal(0,.001,len(df))})
model=LinearRegression().fit(X,df.duration)
answer=pd.Series(model.coef_,index=X.columns)
The tiny perturbation preserves strong correlation; inspecting both coefficients exposes instability that prediction quality alone can conceal.
Helpful prior knowledge: Read coefficients after encoding These links are guidance, not locks.
Sources and API context
Examples run with this Playground’s scikit-learn 1.4.2 / Pyodide 0.26.4 runtime.